### G-2005-81

# A Note on the Definition of a Linear Bilevel Programming Solution

## Charles Audet, Jean Haddad, and Gilles Savard

An alternative definition of the linear bilevel programming problem *BLP* has recently
been proposed by Lu, Shi, and Zhang. This note shows that the proposed
definition is a restriction of *BLP*. Indeed, the new definition is equivalent to transferring
the first-level constraints involving second-level variables into the second level,
resulting in a special case of *BLP* in which there are no first-level constraint involving
second-level variables. Thus, contrary to what is stated by the authors who suggested
the new definition, this does not allow to solve a wider class of problems, but rather
relaxes the feasible region, allowing for infeasible points to be considered as feasible.

Published **October 2005**
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8 pages